Work on Python 3.13 support in PyTorch for the default CPython build is in progress: pytorch/pytorch#130249. It currently builds from source; there's a draft PR for Linux nightlies. Once those land, that prerequisite is met. pytorch/pytorch#130249 also contains top-level tracking items for free-threaded support.

There are also be dependencies that are missing support or only have it in main/nightlies (e.g., psutil, pyyaml, numpy). Also a python package in a Conda channel will be very helpful, because the recommended PyTorch development is with conda due to the many non-Python dependencies (MKL, CUDA, etc.).